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a lift uniformly accelerates at a m/s 2 , then has uniform velocity for some time and finally , retards uniformly at a m/s 2 to come to rest .If the total time taken is T and the total height reached is H ,then prove that the time in which the car has has uniform velocity is (T 2 -4H/a) 0.5

a lift uniformly accelerates at a m/s2 , then has uniform velocity for some time and finally , retards uniformly at a m/s2 to come to rest .If the total time taken is T and the total height reached is H ,then prove that the time in which the car has has uniform velocity is (T2 -4H/a)0.5

Grade:11

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
Let us assume the following:
s_{1}=\frac{1}{2}at_{1}^{2}, v_{1}=at_{1}, s_{2}=v_{1}t_{2}, s_{3}=v_{1}t_{3}-\frac{1}{2}at_{3}^{2}
Hence, we get:
v_{1}=at_{3}, H=v_{1}\left ( t_{1}+t_{2} \right ), T=2t_{1}+t_{2}}
using this, we get:
t_{2}=\pm \sqrt{T^{2}-4\frac{H}{a}}
Regards
Sumit

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